# A Theoretical Study on Friction of Macroscale Patterned Surfaces: Implications for Scaling Up Superlubricity

## TL;DR

This paper explores how to scale up superlubricity, a nearly frictionless state, from the microscale to the macroscale using patterned surfaces and theoretical models.

## Contribution

The study introduces a theoretical framework and simulations to understand and optimize macroscale superlubricity through patterned surfaces.

## Key findings

- Friction behavior is influenced by bump radius, coating durability, and surface elasticity.
- Analytical scaling laws align with simulation results for macroscopic load parameters.
- Height variations in surface patterns affect frictional performance under imperfect conditions.

## Abstract

“Structural superlubricity”, a state of
frictionless
sliding between crystalline surfaces, has been observed at the nanoscale
and microscale. However, achieving it at the macroscale requires further
investigation. Inspired by recent experimental studies, we theoretically
examine the friction behavior of macroscale patterned surfaces composed
of microscale bumps coated with superlubricious two-dimensional materials.
We performed numerical simulations with the discrete element method.
The Hertz contact model, along with a modified tangential Mindlin
contact model, is employed to capture the nonlinear relationship between
the coefficient of friction and normal load. Our results reveal that
the friction behavior is significantly influenced by the radius of
the microscale bumps, the durability of the coating, and the elasticity
of the surface, and we show how those can be tuned to improve friction
properties. Additionally, we analytically investigate the deformation
mechanisms of the surface structure and derive scaling laws for parameters
and the breakdown of superlubricity. The simulation results show strong
agreement with the analytical derivations of power laws for scaling
of various quantities with the total macroscopic load. Finally, we
examine imperfect conditions by investigating how height variations
impact frictional performance.